Why do some Muslim converts change their whole names and others only part?

Al-Qaida spokesman Adam Yahiye Gadahn released a video last Sunday in which he called President Obama a "treacherous, bloodthirsty, and narrow-minded American war president" of a "declining and besieged empire." Numerous reports suggest that Gadahn was born with the name Adam Pearlman, in California. Why do some converts to Islam change part of their name, but not the whole thing?